Finite Group Databasebeta

← #11805674

Subgroups — #11805674

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 711 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4987C211yesmaximal, characteristic, complemented
5C3×#4977C211yesmaximal, characteristic, complemented
6#10591368C212yesmaximal, complemented
7#10591364C212yesmaximal
8#10591335C212yesmaximal, complemented
9#10591325C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591259C212yesmaximal, complemented
12#74229—31nomaximal
13#73883—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yes—
22#64101—24no—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×#3722C2212yes—
30C2×#3722C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×Dic32C2212yes—
33C4×#626C418yescomplemented
34D3×C4⋊Dic3—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C4×#67—31no—
41C22×C4⋊Dic3—31no—
42C2×#892—31no—
43C2×#892—31no—
44C2×#892—61no—
45C2×D3×C4⋊C4—31no—
46C2×C4×D12—31no—
47C3×#382—31no—
48C3×#380—31no—
49#4987—31no—
50#4987—31no—
51#4987D311yescharacteristic, complemented
52#4977D311yescharacteristic, complemented
53Dic3×C4⋊C4—31no—
54#4958—32no—
55Dic3×C22⋊C4—32no—
56C4×C4⋊Dic3—31no—
57#4670—32no—
58#4669—32no—
59#4666—32no—
60#4665—32no—
61#4655—32no—
62#4654—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2×C414yescomplemented
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yes—
80C2×#626—22no—
81C2×#626—22no—
82C2×#626C2×C414yes—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—42no—
86C32×C4⋊C4—22no—
87#3752—24no—
88C4⋊(C3⋊Dic3)D414yescomplemented
89C4×C3⋊Dic3—24no—
90C3×(C2×D3)⋊C4—24no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3—22no—
93C3×C4×Dic3C2×C414yescomplemented
94Dic3⋊Dic3—24no—
95Dic3⋊Dic3C2×C414yescomplemented
96#3722—42no—
97#3722C2×C414yescomplemented
98(C2×D3)⋊Dic3C2×C414yes—
99Dic32—42no—
100#2352—91noSylow
101C23×C3×C4—31no—
102C22×#67—31no—
103C23×Dic3—32no—
104C22×D12—31no—
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—32no—
108C22×C4×D3—61no—
109C22×C4×D3C2×D311yescharacteristic
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4—32no—
116C2×C3×C42—31no—
117C2×#217—31no—
118C4×#67—38no—
119C2×(C2×D3)⋊C4—31no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—62no—
127C2×(C2×D3)⋊C4C2×D312yes—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3—64no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—62no—
143C2×C4×Dic3C2×D311yescharacteristic
144#892—64no—
145#892—64no—
146#892—68no—
147D3×C4⋊C4—64no—
148C4×D12—38no—
149C3×#95—32no—
150C3×#95—32no—
151C3×#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D312yes—
157C3⋊#95C2×D312yes—
158C3⋊#95C2×D312yes—
159C23×C32C2411yescharacteristic
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3C22×C412yes—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3C22×C412yes—
172C22×C3×D3#4112yes—
173C22×C3×D3#4112yes—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4#4112yes—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3C22×C412yes—
185C2×C3⋊Dic3C2×D414yes—
186C4×C3⋊D3—28no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C22×C412yes—
201C2×C3×Dic3C22×C412yes—
202C3×C4×D3—28no—
203#626—28no—
204D3×Dic3—48no—
205C2×C4×D4—91no—
206C2×#117—91no—
207C22×C4⋊C4—91no—
208#388—92no—
209#387—92no—
210#386—92no—
211#382—31no—
212#380—31no—
213#380—91no—
214C4×C4⋊C4—91no—
215C4×C22⋊C4—92no—
216C24×C3—31no—
217C23×D3—31no—
218C23×D3—31no—
219C23×D3—61no—
220C23×D3C22×D311yescharacteristic
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—34no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—34no—
236C2×#67—62no—
237C2×#67—62no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—61no—
243C22×Dic3—62no—
244C22×Dic3—64no—
245C22×Dic3—64no—
246C22×Dic3—122no—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D311yescharacteristic
250C22×Dic3C22×D311yescharacteristic
251C22×Dic3C22×D311yescharacteristic
252C2×D12—34no—
253C2×D12—62no—
254C2×D12—62no—
255C2×C4×D3—22no—
256C2×C4×D3—22no—
257C2×C4×D3—34no—
258C2×C4×D3—34no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—64no—
267C2×C4×D3—64no—
268C2×C4×D3—122no—
269C2×C4×D3C4×D314yes—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—62no—
274C3×C4⋊C4—62no—
275C3×C22⋊C4—64no—
276C3×C42—34no—
277#217—34no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—34no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—68no—
285(C2×D3)⋊C4—122no—
286(C2×D3)⋊C4—122no—
287C4⋊Dic3—22no—
288C4⋊Dic3—22no—
289C4⋊Dic3—34no—
290C4⋊Dic3—34no—
291C4⋊Dic3—34no—
292C4⋊Dic3—64no—
293C4⋊Dic3—64no—
294Dic3⋊C4—34no—
295Dic3⋊C4—64no—
296C4×Dic3—64no—
297C4×Dic3—64no—
298C4×Dic3—68no—
299C4×Dic3—122no—
300C4×Dic3—122no—
301C4×Dic3C4×D314yescomplemented
302C22×C32C23×C411yescharacteristic
303C22×C32C22×D411yescharacteristic
304C22×C32C2×#4111yescharacteristic
305C22×C32C2×#4111yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C22×C32H(5,𝔽2)11yescharacteristic
308C22×C322−1+411yescharacteristic
309C2×C3⋊D3—22no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3—41no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3#11714yescomplemented
323C32×C4—42no—
324C32×C4C4×D414yes—
325C3⋊Dic3—22no—
326C3⋊Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—22no—
329C3×Dic3—22no—
330C3×Dic3—42no—
331C3×Dic3—42no—
332C22×D4—91no—
333C23×C4—31no—
334C23×C4—92no—
335C23×C4—91no—
336C4×D4—98no—
337#117—184no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—92no—
343C2×C4⋊C4—184no—
344C2×C4⋊C4D3211yescharacteristic
345C2×C22⋊C4—32no—
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—92no—
349C2×C22⋊C4—92no—
350C2×C42—31no—
351C2×C42—92no—
352C2×C42—92no—
353#95—32no—
354#95—32no—
355#95—32no—
356#95—92no—
357#95—92no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—32no—
361C23×C3—32no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3C23×D311yescharacteristic
367C23×C3C23×D311yescharacteristic
368C22×D3—21no—
369C22×D3—21no—
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—32no—
373C22×D3—32no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—61no—
388C22×D3—61no—
389C22×D3—121no—
390C22×D3—121no—
391C22×D3—121no—
392C22×D3—121no—
393C22×D3C2×C4×D312yes—
394C22×D3#23712yes—
395C22×D3#23912yes—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—32no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—68no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4C2×C4×D312yes—
425C2×C3×C4C2×C4×D312yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4#23712yes—
429C2×C3×C4#23912yes—
430#67—68no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—34no—
446C2×Dic3—34no—
447C2×Dic3—62no—
448C2×Dic3—64no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—122no—
460C2×Dic3—122no—
461C2×Dic3—128no—
462C2×Dic3C2×C4×D312yes—
463C2×Dic3C2×C4×D312yes—
464C2×Dic3C2×C4×D312yes—
465D12—68no—
466C4×D3—28no—
467C4×D3—616no—
468C4×D3—68no—
469C4×D3—68no—
470C4×D3—128no—
471C2×C32C2×#11711yescharacteristic
472C2×C32C2×C4×D411yescharacteristic
473C2×C32#52011yescharacteristic
474C2×C32#54611yescharacteristic
475C2×C32#54811yescharacteristic
476C2×C32#55211yescharacteristic
477C2×C32#55311yescharacteristic
478C3⋊D3—42no—
479C3×D3—24no—
480C24—31no—
481C24—91no—
482C2×D4—94no—
483C2×D4—182no—
484C2×D4—182no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—34no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—91no—
494C22×C4—92no—
495C22×C4—94no—
496C22×C4—184no—
497C22×C4—184no—
498C22×C4—182no—
499C22×C4—182no—
500C22×C4—362no—
501C22×C4C2×D3212yes—
502C22×C4C2×D3211yescharacteristic
503C4⋊C4—22no—
504C4⋊C4—62no—
505C4⋊C4—62no—
506C4⋊C4—94no—
507C4⋊C4—94no—
508C4⋊C4—184no—
509C22⋊C4—64no—
510C22⋊C4—94no—
511C22⋊C4—94no—
512C22⋊C4—184no—
513C22⋊C4—362no—
514C42—34no—
515C42—184no—
516C42—362no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—34no—
525C22×C3—62no—
526C22×C3—62no—
527C22×C3—62no—
528C22×C3—62no—
529C22×C3—62no—
530C22×C3—62no—
531C22×C3C22×C4×D311yescharacteristic
532C22×C3C22×C4×D311yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×D3×D411yescharacteristic
535C22×C3C2×#23711yescharacteristic
536C22×C3C2×#23711yescharacteristic
537C22×C3C2×#23911yescharacteristic
538C22×C3C2×#23911yescharacteristic
539C22×C3D3×#4111yescharacteristic
540C22×C3D3×#4111yescharacteristic
541C22×C3#100911yescharacteristic
542C22×C3#100911yescharacteristic
543C22×C3#101011yescharacteristic
544C22×C3#101011yescharacteristic
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—64no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—62no—
556C2×D3—62no—
557C2×D3—62no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—121no—
571C2×D3—121no—
572C2×D3#89214yescomplemented
573C3×C4—24no—
574C3×C4—44no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—62no—
578C3×C4—62no—
579C3×C4—62no—
580C3×C4—122no—
581C3×C4—122no—
582C3×C4#67⋊C414yes—
583C3×C4#89314yes—
584Dic3—22no—
585Dic3—22no—
586Dic3—22no—
587Dic3—42no—
588Dic3—42no—
589Dic3—64no—
590Dic3—64no—
591Dic3—62no—
592Dic3—62no—
593Dic3—64no—
594Dic3—124no—
595C32#235211yescharacteristic, complemented, Sylow
596C23—32no—
597C23—32no—
598C23—32no—
599C23—61no—
600C23—61no—
601C23—61no—
602C23—61no—
603C23—92no—
604C23—181no—
605C23—181no—
606C23—181no—
607C23—181no—
608C23—181no—
609C23—181no—
610C23C22×D3211yescharacteristic
611D4—188no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—32no—
616C2×C4—32no—
617C2×C4—32no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—68no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—92no—
632C2×C4—94no—
633C2×C4—181no—
634C2×C4—182no—
635C2×C4—182no—
636C2×C4—181no—
637C2×C4—188no—
638C2×C4—368no—
639C2×C4#379612yes—
640C2×C4C4×D3212yes—
641C2×C4#381112yes—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—64no—
650C2×C3C2×#67⋊C411yescharacteristic
651C2×C3C2×#89211yescharacteristic
652C2×C3C2×#89311yescharacteristic
653C2×C3D3×#11711yescharacteristic
654C2×C3#552311yescharacteristic
655C2×C3#552311yescharacteristic
656C2×C3#559811yescharacteristic
657C2×C3#561811yescharacteristic
658C2×C3#563011yescharacteristic
659C2×C3#564211yescharacteristic
660C2×C3#567611yescharacteristic
661C2×C3#567711yescharacteristic
662C2×C3#569411yescharacteristic
663C2×C3#569511yescharacteristic
664D3—24no—
665D3—124no—
666D3—122no—
667D3—122no—
668C22—34no—
669C22—62no—
670C22—62no—
671C22—62no—
672C22—62no—
673C22—62no—
674C22—62no—
675C22—182no—
676C22—182no—
677C22—182no—
678C22—361no—
679C22—361no—
680C22—361no—
681C22—361no—
682C22C2×#379611yescharacteristic
683C22C2×C4×D3211yescharacteristic
684C22#6430911yescharacteristic
685C22D3×#23711yescharacteristic
686C22D3×#23911yescharacteristic
687C22#6432011yescharacteristic
688C22C2×#381111yescharacteristic
689C4—42no—
690C4—62no—
691C4—62no—
692C4—62no—
693C4—122no—
694C4—122no—
695C4—182no—
696C4—184no—
697C4#6388114yes—
698C3—21no—
699C3#7388311yescharacteristic, complemented
700C3#7422911yescharacteristic, complemented
701C2—64no—
702C2—362no—
703C2#1059443711yescharacteristic
704C2#1059445711yescharacteristic
705C2#1059451111yescharacteristic
706C2D3×#89211yescharacteristic
707C2C2×#6388111yescharacteristic
708C2#1059516111yescharacteristic
709C2#1059543111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64101C2semidirect
3. C2×D3×C4⋊Dic3C2semidirect
4. C3×#4987C2semidirect
5. C3×#4977C2semidirect
6. #10591368C2semidirect
8. #10591335C2semidirect
9. #10591325C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591259C2semidirect
33. C4×#626C4semidirect
51. #4987D3semidirect
52. #4977D3semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
88. C4⋊(C3⋊Dic3)D4semidirect
93. C3×C4×Dic3C2×C4semidirect
95. Dic3⋊Dic3C2×C4semidirect
97. #3722C2×C4semidirect
301. C4×Dic3C4×D3semidirect
322. C2×C3×D3#117semidirect
572. C2×D3#892semidirect
595. C32#2352semidirect
699. C3#73883semidirect
700. C3#74229semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#641012
C2×C4×#6262
C2×D3×C4⋊Dic32
C3×#49872
C3×#49772
#105913682
#105913642
#105913352
#105913252
Dic3×C4⋊Dic32
#105912592
#742293
#738833